PS3 Modding

First off, you must have a PS3 on FirmWare 3.55, or lower, to mod it. If you are on a lower FW, then simply upgrade to 3.55. However, if you're on a higher FW, then you must downgrade using a hardware Flasher. Below is table for what models are downgradable and what flashers can be used on those models:

Basically, all fat models are downgradable, if you have a NAND model (CECH-A to CECH-G) use Teensy++ and if you have a NOR model (CECH-H to CECH-Q or any downgradable slim PS3) use E3 Flasher. For downgrading I suggest you follow a tutorial: Using Teensy++/Progskeet or Using E3 Flasher

Also, once you are on FW 3.55 you'll have to enter Factory Service Mode, to do that either follow this (see Chapter 2, Part 1), or use one of these devices.

You can connect to PSN while on CFW, but there is a high risk that your PSN ID and Console ID will be banned. There is a way to unban your console though... it requires someone else's Console ID and if that gets banned too, you'll end up banning them.